How expensive, tens, hundreds, thousands?
That depends on whether you hire a professional SW developer to do something original from the ground up, or some slightly-experienced student arduino hacker that’s willing to gather the existing free examples into something that almost works. You can figure that a fully-burdened (ie some who makes their living as a consultant, and has to pay their own payroll taxes and business expenses) US-based professional embedded developer costs abotu $100k/y (call that $50/h.) Less for non-US, less-professional… Plus expenses, of course.
And it depends on how well you can explain what you want. Because each time you go back and say “almost, now can you make it do Y” is more hours - potentially a LOT more hours if Y is much different than the starting goal. People who haven’t done SW development are typically not very good at defining software either, leading to frustration on both sides.
So … hundreds to 10s of thousands, probably.
Now, you CAN be sneaky and see if you can get volunteers to “implement open source software for this neat idea”, and maybe not spend anything - just look at what has been contributed to the (greater) arduino project for free. I’ve done “will write code for toys” (send me hardware and I’ll make it do stuff" projects that I thought worked out really well, plus “wouldn’t it be nice if the bootloader did XX” and similar. But …